This proposal intends to develop flexible nonparametric regression methods and statistical inference tools for modeling long-term HIV and T lymphocyte dynamics in HIV-1 -infected patients treated with highly active antiretroviral therapies (HAART). The first specific aim is to develop flexible and efficient nonparametric regression models and inference tools for longitudinal HIV/T-cell dynamic data. These include: (1a) to develop flexible and efficient nonparametric regression methods for longitudinal data. These will include the investigation and extension of local kernel regression methods and basis-based regression splines methods for longitudinal data analysis; (1b) to study the asymptotic and finite-sample properties of the developed nonparametric estimation methods. To compare and evaluate different methods, and to propose the best one for practical use; (1c) to develop statistical inference methods for nonparametric regression models with longitudinal data; (Id) to develop computer programs or software to implement the proposed methodologies. The second aim is to apply the developed methods to study long-term HIVTT-cell dynamics using the data from AIDS clinical trials developed by the AIDS Clinical Trials Group (ACTG). These include: (2a) to characterize long-term HIVTT-cell dynamics in HIV-I-infected patients treated with HAART using flexible nonparametric regression methods for longitudinal data, and to study the relationship between long-term HIV dynamics and T lymphocyte kinetics in the environment of long-term antiretroviral drug exposure; (2b) to identify what pharmacological, clinical and host-specific factors affect the long-term dynamics of HIV and T lymphocytes; (2c) to study the relationships between clinical endpoints and the long-term dynamic patterns of HIV and T lymphocytes; (2d) to explore how the long-term HIV/T-cell dynamic patterns can be used to assess the long-term effectiveness of antiretroviral therapies. We may gain more and deep understanding of pathogenesis of chronic HIV infection via modeling the long-term dynamics of HIV and T cells. We expect that the results from this project can be used to assess the long-term effectiveness of antiretroviral therapies and provide information for long-term care and treatment management for HIV-I-infected patients.